### Abstract

For nearly 70 years, the solution to the discrete ordinates approximation of the ID monoenergetic neutron transport equation has been an effective approximation. During that time, the method has experienced numerous improvements as numerical and computational techniques have advanced. Here, we propose a new, consistent expression of the analytical solution to the ID, monoenergetic discrete ordinates (DOM) equations, called the Response Matrix DOM (RM/DOM), which is an improvement over past forms. The approach takes advantage of the second order form of the discrete ordinates approximation to express the solution as hyperbolic functions rather than ordinary exponentials. By comparison, a highly anisotropic radiative transfer benchmark will demonstrate the precision of the solution. We then establish a new high order benchmark for scattering in a purely hydrogenous medium and apply RM/DOM to general monoenergetic elastic scattering.

Original language | English (US) |
---|---|

Title of host publication | Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015 |

Publisher | American Nuclear Society |

Pages | 1327-1338 |

Number of pages | 12 |

Volume | 2 |

ISBN (Print) | 9781510808041 |

State | Published - 2015 |

Event | Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015 - Nashville, United States Duration: Apr 19 2015 → Apr 23 2015 |

### Other

Other | Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015 |
---|---|

Country | United States |

City | Nashville |

Period | 4/19/15 → 4/23/15 |

### Fingerprint

### Keywords

- Anisotropic scattering
- Convergence acceleration
- Diagonalization
- Second order ODE

### ASJC Scopus subject areas

- Mathematics(all)
- Nuclear and High Energy Physics

### Cite this

*Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015*(Vol. 2, pp. 1327-1338). American Nuclear Society.

**Response matrix solution to discrete ordinates approximation of the ID monoenergetic neutron transport equation.** / Ganapol, Barry D.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015.*vol. 2, American Nuclear Society, pp. 1327-1338, Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015, Nashville, United States, 4/19/15.

}

TY - GEN

T1 - Response matrix solution to discrete ordinates approximation of the ID monoenergetic neutron transport equation

AU - Ganapol, Barry D

PY - 2015

Y1 - 2015

N2 - For nearly 70 years, the solution to the discrete ordinates approximation of the ID monoenergetic neutron transport equation has been an effective approximation. During that time, the method has experienced numerous improvements as numerical and computational techniques have advanced. Here, we propose a new, consistent expression of the analytical solution to the ID, monoenergetic discrete ordinates (DOM) equations, called the Response Matrix DOM (RM/DOM), which is an improvement over past forms. The approach takes advantage of the second order form of the discrete ordinates approximation to express the solution as hyperbolic functions rather than ordinary exponentials. By comparison, a highly anisotropic radiative transfer benchmark will demonstrate the precision of the solution. We then establish a new high order benchmark for scattering in a purely hydrogenous medium and apply RM/DOM to general monoenergetic elastic scattering.

AB - For nearly 70 years, the solution to the discrete ordinates approximation of the ID monoenergetic neutron transport equation has been an effective approximation. During that time, the method has experienced numerous improvements as numerical and computational techniques have advanced. Here, we propose a new, consistent expression of the analytical solution to the ID, monoenergetic discrete ordinates (DOM) equations, called the Response Matrix DOM (RM/DOM), which is an improvement over past forms. The approach takes advantage of the second order form of the discrete ordinates approximation to express the solution as hyperbolic functions rather than ordinary exponentials. By comparison, a highly anisotropic radiative transfer benchmark will demonstrate the precision of the solution. We then establish a new high order benchmark for scattering in a purely hydrogenous medium and apply RM/DOM to general monoenergetic elastic scattering.

KW - Anisotropic scattering

KW - Convergence acceleration

KW - Diagonalization

KW - Second order ODE

UR - http://www.scopus.com/inward/record.url?scp=84949506489&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84949506489&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84949506489

SN - 9781510808041

VL - 2

SP - 1327

EP - 1338

BT - Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015

PB - American Nuclear Society

ER -